中文摘要：

Let Mn（n ≥ 4） be an oriented closed submanifold with parallel mean curvature in an（n + p）-dimensional locally symmetric Riemannian manifold Nn+p. We prove that if the sectional curvature of N is positively pinched in [δ, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ = 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu[15].更多还原

英文摘要：

Let Mn（n ≥ 4） be an oriented closed submanifold with parallel mean curvature in an （n ＋ p）-dimensional locally symmetric Riemannian manifold Nn＋p. We prove that if the sectional curvature of N is positively pinched in [5, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ= 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu [15].